Beside this I have another domain www.example.org on which I want to run the same shop. I am facing some problems/questions:

1. Do I need a SSL certificate for each domain or can I share one for the shop?
2. Will the orders coming from www.example.com be visible in the shop on www.example.org and vice versa? I am asking because I do not want to check both domains for new orders - I want to have it all in one system
3. Would it be a better idea to create one shop on a subdomain e.g www.shop.example.com and redirect to it from both domains?